core: share responses request builder with compact requests (#20989)

## Why

`ModelClientSession` and `compact_conversation_history()` were still
rebuilding the same `ResponsesApiRequest` fields separately. That
duplication makes it easy for normal `/responses` turns and compact
requests to drift when request-shape changes land later, which is
exactly the kind of cache-affecting divergence we want to avoid.

This follow-up keeps the scope small by extracting the shared
request-construction logic into one helper and using it from both paths.

## What changed

- move `ResponsesApiRequest` construction into a shared
`ModelClient::build_responses_request(...)` helper in
`core/src/client.rs`
- update the normal `/responses` streaming path to call that helper
instead of the old `ModelClientSession`-local implementation
- update `compact_conversation_history()` to derive its compact payload
from the same helper so `model`, `instructions`, `input`, `tools`,
`parallel_tool_calls`, `reasoning`, and `text` stay aligned with normal
request building
- add a unit test covering the shared helper's prompt cache key,
installation metadata, and `service_tier` behavior

## Verification

- `cargo test -p codex-core
build_responses_request_sets_shared_cache_and_metadata_fields`
- `cargo test -p codex-core --test all
remote_compact_v2_reuses_context_compaction_for_followups`

## Docs

No docs update needed.

codex-rs/core/tests/suite/client.rs

@@ -770,10 +770,15 @@ async fn includes_conversation_id_and_model_headers_in_request() {
     let installation_id =
         std::fs::read_to_string(test.codex_home_path().join(INSTALLATION_ID_FILENAME))
             .expect("read installation id");
+    let session_id_string = session_id.to_string();
 
-    assert_eq!(request_session_id, session_id.to_string());
+    assert_eq!(request_session_id, session_id_string);
     assert_eq!(request_originator, originator().value);
     assert_eq!(request_authorization, "Bearer Test API Key");
+    assert_eq!(
+        request_body["prompt_cache_key"].as_str(),
+        Some(session_id_string.as_str())
+    );
     assert_eq!(
         request_body["client_metadata"]["x-codex-installation-id"].as_str(),
         Some(installation_id.as_str())